1. Technical Field
The present invention relates generally to apparatus and methods for processing information-bearing signals corrupted by noise. More particularly, the present invention relates to a signal processing apparatus and method which can be used to correct signal amplitude level variations, restoring them to receiver optimal design levels.
2. History of Related Art
Chaotic processes applied to information-bearing signals have properties that provide low probability of intercept (LPI) and low probability of detection (LPD), making them a natural choice as the foundation of communications systems. Chaotic signals have the prima facie appearance of noise for LPD, extreme sensitivity to initial conditions for LPI, and dynamics rendering receivers relatively intolerant of signal amplitude variations.
Communications systems based on chaotic processes have improved significantly in the decade since chaotic synchronization was first achieved. Several methods of synchronization combine with various modulation techniques to produce secure communication using signals in analog and digital form (e.g. Chua""s circuit and chaotic maps, respectively). However, since chaotic processes are extremely sensitive to signal amplitude variation, chaotic receivers tend to lose synchronization and data recovery capabilities at variation levels as small as +/xe2x88x923 dB. Thus, the inability to communicate beyond shouting distance has kept chaos-based communications systems in the laboratory.
There has been some work directed toward addressing this xe2x80x9cdistance problemxe2x80x9d, such as Tom Carroll""s customized chaotic process that achieves amplitude-independent synchronization (see xe2x80x9cAmplitude Independent Chaotic Synchronization and Communication,xe2x80x9d in Chaotic Circuits for Communication, Proceedings of the SPIE 2612, pp. 181-188, 1995). The need to customize chaos to achieve some degree of amplitude variation tolerance is a restrictive requirement, though, and an apparatus or method that works with an arbitrary or unrestricted chaotic process is highly desirable.
Since all communication systems are susceptible to interfering signals normally referred to as noise, the problem of chaotic signal reception can become even more difficult. Interfering signals may have harmful effects on the performance of any communication system, depending on the specific system being used, the nature of the noise, and the way the noise interacts with the signal. The magnitude of these effects is also determined by the relative intensity of the noise compared to the signal, which is usually measured as the signal-to-noise-ratio (SNR), or the ratio of the power of the signal to the power of the noise. Such effects are magnified with respect to chaotic systems, given the extreme sensitivity to signal level variation.
Communications receivers, which demodulate a signal to recover its information content, employ demodulation techniques whose designs are based on the statistics of both the signal and the corrupting noise. This approach has its roots in the Shannon channel capacity theorem, which states that channel capacity is a function of SNR. There are a variety of methods for the recovery of data corrupted by random noise, including maximum likelihood (ML) decision generators, also known as maximum a priori detectors; maximum a posteriori (MAP) detectors; minimum Euclidean distance calculators; correlation receivers; cross-correlation detectors; and matched filter detectors. While all techniques derive from the noise statistics, not all algorithms explicitly calculate noise power or SNR. Estimates of the noise power are typically used to derive SNR in order to estimate the quality of the receiver output; and they sometimes aid in the data recovery process, as with critical applications employing the MAP detector. Two examples of quality metrics calculated from SNR estimates are (1) a bit error rate (BER) and (2) a GPS navigation solution accuracy approximation.
Prior techniques of calculating SNR have involved various methods of estimating noise power and signal power individually, and dividing them to find the signal-to-noise ratio. For example, a binary phase-shift-key modulation technique or a direct sequence spread spectrum chipping code utilize a voltage for a logical one, and the negative of the voltage for a logical zero at baseband. Subtraction of sequential values is one method of estimating the noise content of such a received signal, and squaring the estimated noise voltages yields the noise power. Chaotic processes, however, associate a logical state with a noise-like sequence of values, rather than a single voltage level. This deterministically random characteristic of chaotic signals precludes the use of prior noise estimation methods, because the continuum of values corresponding to a logical state is not amenable to noise estimation methods that are based on the association of a constant quantity with a logical state. As a result, estimates of the individual signal power and noise power could not be made by conventional techniques.
The design of a new chaotic receiver utilizing a MAP detector requires knowledge of the noise statistics, specifically mean and power, so as to construct a window to superimpose on the chaotic transmit Probability Density Function (PDF). Investigation of the received PDF yielded observations of a relationship between received values and SNR. This relationship was developed and exploited to enable the estimation of SNR directly from received values, without the need to first estimate the individual signal and noise power values, solving the implementation dilemma for using a MAP detector with a chaotic receiver operating in a lossless channel.
Chaotic systems, however, have been observed to lose synchronization with as little as +/xe2x88x923 dB amplitude variation, and so are intolerant of the propagation losses and processing losses and/or gains that are integral to real communications systems operating in lossy channels. The new SNR estimation method had no means of separating the signal power from the noise power. The receiver design was, therefore, relegated to the same status of laboratory curiosity as the other chaotic designs.
Thus a method and apparatus which enables the isolation of the message signal power from the noise power in a received signal, estimating the received message signal power deviations from receiver design values, generating a correction factor, and scaling the received signal to the proper level for optimal receiver operation would be highly beneficial. Such a method and apparatus would accurately adjust for signal attenuation and amplification via the correction factor so as to restore received signals to optimal levels, even in the face of amplitude deviations due to transmitter amplification and propagation losses. Even more beneficial would be the provision of a generalized technique, usable with receivers of linear, nonlinear, and/or nonlinear chaotic design. Such a method and apparatus would be most useful if the only a priori knowledge required to accomplish signal amplitude restoration were a transmit signal probability density function (PDF) and the optimum receiver design operational power level. Since the SNR is typically calculated in many communications applications, the apparatus and method might also make use of this ratio for estimating results such as message recovery fidelity, circular error probability for global positioning satellite systems (GPS), and receiver-feedback transmit power level control.
The apparatus of the present invention for signal amplitude restoration, having a received signal input and a scaled received signal output, includes an amplitude correction factor generator which has an estimated signal-to-noise power ratio input and a received signal input; a variable gain amplifier which uses the correction factor generator output to control its gain, and which amplifies or attenuates the received signal input to provide the scaled received signal output; and an average SNR estimator which uses the amplifier output as its input, and provides an output connected to the estimated signal-to-noise power ratio input. The apparatus and method operate to process received signals in an iterative fashion, such that at least one of the outputs is stored for use as a feedback input during later iterations.
The amplitude correction factor generator, in turn, is made up of a received power estimator connected to the received signal input, a message signal power estimator connected to the received power estimator and the estimated signal plus noise power ratio input, and a scaling correction factor generator connected to the message signal power estimator and the gain control of the amplifier. The average SNR estimator comprises, in turn, a SNR maximum likelihood estimator connected to the scaled received signal output, a received likelihood detector connected to the scaled received signal output and the SNR maximum likelihood estimator, and a running weighted averager connected to both the SNR maximum likelihood estimator and the received likelihood detector, so as to provide an output connected to the message signal power estimator (typically contained within the amplitude correction factor generator) and the SNR maximum likelihood estimator. A unit delay element is used to store the output of the running weighted averager as an input to the message signal power estimator on subsequent iterations.
The method of the present invention for providing a level-restored received signal output comprises the steps of providing a correction factor output to the gain control of a variable gain amplifier (connected to the received signal input), and providing an average signal-to-noise ratio (SNR) estimate using the level-restored received signal output and a stored running weighted average from a previous iteration of the method for feedback to a correction factor generator (which provides the correction factor output). The resulting average SNR estimate is stored as a new running weighted average for use in subsequent iterations of the method.
Providing a correction factor output may include estimating a signal plus noise power output as approximately equal to the summation of the received signal input squared over a preselected time interval window; estimating the signal power output as approximately equal to a product of the signal plus noise power output and the stored running weighted average divided by a quantity of one plus the stored running weighted average; and calculating the correction factor output as approximately inversely proportional to a square root of the signal power output, and most preferably, as approximately equal to a square root of the preselected receiver design power level divided by the square root of the signal power output. Providing an average SNR estimate may include estimating the SNR maximum likelihood output using the level-restored received signal output and the stored running weighted average; determining a received likelihood detector output using the level-restored received signal output and the SNR maximum likelihood output; and determining a new running weighted average using the received likelihood detector output, the SNR maximum likelihood output, and a plurality of weighting values, each value being approximately equal to an incremental probability of the occurrence of the current scaled received value with the current maximum likelihood SNR, raised to an empirically-derived power.
The method and apparatus described herein provide a new paradigm for the restoration of chaotic signals corrupted by random noise. Using a direct SNR estimator which requires only the transmit PDF, and an amplitude correction factor generator which makes use of a preselected receiver design operational power level, the amount of loss/gain in the received signal can be calculated and corrected to optimal receiver design levels. Whereas a prior art chaotic receiver typically loses synchronization whenever chaotic signal levels vary by more than +/xe2x88x923 dB, optimal level restoration using the method and apparatus of the present invention has been demonstrated with 200 dB loss (equivalent to a signal transmission distance of 164,000 miles at 900 MHz), through 200 dB gain, preserving synchronization and receiver operation across the entire dynamic range. The full operational dynamic range depends on the resolution and numerical range of the target processor. Accuracy depends on noise content, of course. However, laboratory testing confirms that variations between the corrected signals and the original signals are limited to about xc2x10.2 dB (xc2x15%) rms at or above 20 dB SNR, xc2x10.3 dB (xc2x17%) at 10 dB SNR, and xe2x88x921 dB (xe2x88x9226%) at 0 dB SNR with the chosen averaging window lengths of 1024 values for both the received power estimator running average and the Average SNR Estimator running weighted average used to generate the results shown herein. Other values of accuracy and range of SNR coverage will be observed for different choices of averaging window lengths. The algorithm is additionally dependent on the set of exponential argument values to which the incremental probability is raised; where the appropriate set of values correspond to the current estimate of received SNR on a one-to-one basis, and generally depend on the transmit PDF and the noise level.
The present invention solves the transmission loss intolerance problem of chaotic systems that has prevented their transition out of the laboratory. Robust reception for any digital chaotic receiver design, using arbitrary chaotic systems, is provided. The invention also paves the way for future research and development of sub-unity SNR chaotic receiver capability.